Abstract:
An ensemble of independent numerical solutions enables one to construct a hypersphere around the approximate solution that contains the true solution. The analysis is based on some geometry considerations,
such as the triangle inequality and the measure concentration in the spaces of large dimensions. As a result,
there appears the feasibility for non-intrusive postprocessing that provides the error estimation on the ensemble of solutions. The numerical tests for two-dimensional compressible Euler equations are provided that
demonstrates properties of such postprocessing.
Citation:
A. K. Alekseev, A. E. Bondarev, “On a posteriori estimation of the approximation error norm for an ensemble of independent solutions”, Sib. Zh. Vychisl. Mat., 23:3 (2020), 233–248; Num. Anal. Appl., 13:3 (2020), 195–206
\Bibitem{AleBon20}
\by A.~K.~Alekseev, A.~E.~Bondarev
\paper On a posteriori estimation of the approximation error norm for an ensemble of independent solutions
\jour Sib. Zh. Vychisl. Mat.
\yr 2020
\vol 23
\issue 3
\pages 233--248
\mathnet{http://mi.mathnet.ru/sjvm745}
\crossref{https://doi.org/10.15372/SJNM20200301}
\transl
\jour Num. Anal. Appl.
\yr 2020
\vol 13
\issue 3
\pages 195--206
\crossref{https://doi.org/10.1134/S1995423920030015}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000566356600001}
Linking options:
https://www.mathnet.ru/eng/sjvm745
https://www.mathnet.ru/eng/sjvm/v23/i3/p233
This publication is cited in the following 6 articles:
V. NADOLSKI, “VERIFICATION AND VALIDATION OF A COMPUTER COMPUTATIONAL MODEL FOR THE DESIGN OF BUILDING STRUCTURES”, Herald of Polotsk State University. Series F. Civil engineering. Applied sciences, 2024, no. 2, 42
A. K. Alekseev, A. E. Bondarev, Lecture Notes in Computer Science, 14838, Computational Science – ICCS 2024, 2024, 324
V. V. Nadolskii, “Koeffitsienty nadezhnosti dlya stalnykh elementov, proektiruemykh na osnove kompyuternykh chislennykh modelei”, Vestnik MGSU, 19:10 (2024), 1606
A. K. Alekseev, A. E. Bondarev, “Otsenka lokalnoi pogreshnosti approksimatsii po naboru chislennykh reshenii”, Sib. zhurn. vychisl. matem., 25:4 (2022), 343–358
A. K. Alekseev, A. E. Bondarev, “O metode Pragera-Singa otsenki pogreshnosti approksimatsii”, Preprinty IPM im. M. V. Keldysha, 2021, 025, 22 pp.
A. K. Alekseev, A. E. Bondarev, “On a posteriori error estimation using distances between numerical solutions and angles between truncation errors”, Math. Comput. Simul., 190 (2021), 892–904
Citation in format AMSBIB
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